Click Fraud

17 Pages·2016·2.36 MB·English

Click Fraud
Author(s): Kenneth C. Wilbur and Yi Zhu
Source: Marketing Science, Vol. 28, No. 2 (March-April 2009), pp. 293-308
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/23884264
Accessed: 26-05-2016 21:08 UTC

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at
http://about.jstor.org/terms

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted
digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about
JSTOR, please contact [email protected].
INFORMS is collaborating with JSTOR to digitize, preserve and extend access to Marketing Science
This content downloaded from 128.54.18.48 on Thu, 26 May 2016 21:08:16 UTC
All use subject to http://about.jstor.org/terms
Marketing Science
Vol. 28, No. 2, March-April 2009, pp. 293-308
ISSN 0732-23991 eissn 1526-548X1091280210293 doi 10.1287/mksc.l080.0397
©2009 INFORMS
Click Fraud
Kenneth C. Wilbur, Yi Zhu
Marshall School of Business, University of Southern California, Los Angeles, California 90089
{[email protected], [email protected])
Clic kp afrrtayu dw iesb tsihtee prreavcetniucee so for d eexcehpatuisvteilnyg calnic kadinvge rotnis esre'asr cbhu dagdest .w Sietahr cthh ea dinvteernttisieorns oafr ee iftohrecre din tcor etarsuinstg tthhaitrd
search engines detect and prevent click fraud even though the engines get paid for every undetected fraudulent
click. We find conditions under which it is in a search engine's interest to allow some click fraud.
Under full information in a second-price auction, if x°/o of clicks are fraudulent, advertisers will lower their
bids by x°/o, leaving the auction outcome and search engine revenues unchanged. However, if we allow for
uncertainty in the amount of click fraud or change the auction type to include a click-through component, search
engine revenues may rise or fall with click fraud. A decrease occurs when the keyword auction is relatively
competitive because advertisers lower their budgets to hedge against downside risk. If the keyword auction is
less competitive, click fraud may transfer surplus from the winning advertiser to the search engine. Our results
suggest that the search advertising industry would benefit from using a neutral third party to audit search
engines' click fraud detection algorithms.
Key words: advertising; auctions; click fraud; game theory; Internet marketing; search advertising
History: Received: August 8, 2007; accepted: February 19, 2008; processed by Yuxin Chen. Published online in
Articles in Advance October 24, 2008.
1. Introduction question of click fraud is vexing because search
Search advertising revenues grew from virtually noth- engines cannot give advertisers full information about
ing in 1996 to more than $7 billion in 2006, consti- how they detect and prevent click fraud. Doing
tuting 43% of online advertising revenues (Advertising so would be tantamount to providing unscrupulous
Age 2006). The primary benefits of search advertís- advertisers with directions on how to commit click
ing for advertisers are its relevance and accountability. fraud. Advertisers are therefore forced to trust that
It tends to reach consumers as they enter the mar- search engines do their utmost to prevent click fraud,
ket for the advertised product, and advertisers' ability even though the search engines get paid every time
to track consumers' actions online allows for accurate they fail to detect a fraudulent click. This trust was
measurements of advertising profitability. called into question in 2006 when Google CEO Eric
The downside of this accountability is a prac- Schmidt was quoted as saying
tice known as click fraud. Website publishers or Eventually the price that the advertiser is willing to
rival advertisers may impersonate consumers and pay f0r the conversion will decline because the adver
click search ads, driving up advertising costs with- tiser will realize that these are bad clicks. In other
out increasing sales, effectively stealing a firm's paid words, the value of the ad declines. So, over some
advertising inventory. The Click Fraud Network, amount of time, the system is, in fact, self-correcting,
which defines itself as "a community of online adver- 1° lacE there is a perfect economic solution, which is
tisers, agencies and search providers," estimated that to 'et 11 happen (Ghosemajumder 2006).
16.6% of all paid clicks on search engine home pages His remarks were interpreted as suggesting that
and 28.3% of all paid clicks on search engines' content market forces would eliminate any negative effects of
networks in the fourth quarter of 2007 may have been click fraud in the long run, possibly undermining the
fraudulent. Discussions with executives in the search need for ciick fraud detection.1
advertising industry indicate that the amount of click The primary objective of this paper is to understand
fraud varies widely across industries and keywords. how click fraud affects search engines' advertising
The perceived threats of click fraud may outweigh the
benefits of using search advertising for some firms in „ n , , . ., .
° . ° 1 However, Google CFO Ge 1o Hrogweev eRr, eGyooeglse ChFOa dGe oprgre eRveyieos uhasdl ypr evsiaouisdly s1ai dt "hI tihninkk
high-risk categories. something has to be done about [click fraud] really, really quickly,
something has to be done about [click fraud] really, really quickly,
Seventy-three percent of search advertisers say that because I btehcaiunske ,I ptohtinenk,t ipaolltyen, tiital ltyh, riet atthernesa toeunrs obuurs ibnuessins emss omdoedl"e l"(S (tSotnonee
click fraud is a concern (Advertising Age 2006). The 20 02500,5 ,p p. . 5522))..
293
This content downloaded from 128.54.18.48 on Thu, 26 May 2016 21:08:16 UTC
All use subject to http://about.jstor.org/terms
Wilbur and Zhu: Click Fraud
294 Marketing Science 28(2), pp. 293-308, ©2009 INFORMS
revenues. We also hope to gain insights into what matching problem between advertisers and ad slots,
actions search engines may be able to take to mitigate Borgers et al. (2007) generalize advertiser preference
click fraud. We present an analytical model of the auc- functions beyond the previous two papers, finding
tion market for search advertising keywords and then that this implies multiple equilibria, many of which
introduce the possibility that third-party websites or are inefficient. Katona and Sarvary (2007) extend
rival bidders may engage in click fraud. The strengths these analyses by introducing click-through rates into
of our model are its parsimony and generality because the auction mechanism and allowing for interplay
firms' search advertising objectives and the degree of between paid and organic search results,
competition in keyword auctions vary widely across Empirical work on search advertising has focused
keywords. mainly on the link between keyword prices and
We model the elemental unit of competition in the advertiser profitability. Goldfarb and Tucker (2007)
industry: Two advertisers bid in an auction for a sin- show that keyword prices increase in advertisers'
gle advertising slot sold by a monopoly search engine. profitability of advertising and decrease with the
We find that, in a second-price auction, when firms availability of substitute advertising media. Rutz and
know that x% of all clicks will be fraudulent, they Bucklin (2007a) develop a model to enable advertisers
lower their bids by x%. In equilibrium, this adjust- to decide which keywords to keep in a campaign and
ment leaves advertising expenditures and the auc- showed that keyword characteristics and ad position
tion result unchanged. However, when the amount influence conversion rates. Rutz and Bucklin (2007b)
of click fraud is uncertain or when the auction con- show that there are spillovers between search adver
tains a click-through rate component, search engine tising on branded and generic keywords, as some
revenues may increase or decrease with click fraud. customers may start with a generic search to gather
A decrease may occur in relatively competitive key- information, but later use a branded search to corn
word auctions as high bidders hedge their advertising plete their transaction. Ghose and Yang (2007) esti
budgets to protect against the threat of a high real- mate a model of consumer search and advertiser
ization of click fraud. On the other hand, advertis- behavior, linking keyword characteristics to purchase
ing revenues may increase in relatively uncompetitive rates and evaluating the optimality of advertiser bids,
auctions if the foregone profits of exiting the ad auc- We are not aware of any previous analyses of the
tion outweigh the effects of click fraud, resulting in a economic effects of click fraud.
transfer from a very profitable advertiser to the search In the next section we discuss the institutional
engine. details of the industry that guide our analysis. Sec
The surge in Internet usage and advertising rev- tion 3 presents a baseline model of search advertising
enues has attracted substantial academic interest (see, sales in a second-price auction, to which we com
e.g., He and Chen 2006, Iyer and Pazgal 2003, pare click fraud equilibria under various assumptions
Manchanda et al. 2006, Prasad 2007). For example, in §§4 and 5. In §6, we derive click fraud's effects in
Danaher (2007) estimates a comprehensive model of what we call the "click through" auction. Section 7
website-visit behavior based on a large-scale panel provides a nontechnical discussion of the manage
of Internet users, showing how to predict reach and rial implications of our analysis. Section 8 discusses
frequency for various schedules of online adver- limitations and future research opportunities. Proofs
tisements. Theoretical research on search advertising of all lemmas and propositions are contained in the
has focused mainly on competition in advertising appendix,
auctions and consumer search. Baye and Morgan
(2001) analyze a homogeneous-products market orga- 2, Industry Background
nized by a search engine ( gatekeeper ) and show jn this section, we describe the market for search
that the gatekeeper s incentive is to maximize con- advertising, types of click fraud, advertiser percep
sumer adoption but limit the number of advertisers tions of click fraud, and issues in click fraud detection
using the platform because it can extract more rev- ancj measurement
enues when competition among advertisers is less
ened. Chen and He (2006) analyze optimal consumer 2.1. The Search Advertising Marketplace
search and advertiser bid strategies and show that Search advertising, also known as "cost-per-click"
advertisers' bid order mirrors their products' rele- (CPC) or "pay-per-click" advertising, is sold on a
vanee order. Consumers then optimally engage in per-click basis. Advertisers bid on a word or phrase
sequential search. Edelman et al. (2007) solve for equi- related to their business and enter a maximum adver
librium in what they call the "generalized second- tising budget per time period. When consumers
price" auction, a mechanism similar to what Yahoo! enter that "keyword" into a search engine or read a
used to allocate search ads until 2007. Varian (2007) third-party Web page relevant to the keyword, the
independently discovers some similar properties in a advertiser's ad may then be displayed along with
This content downloaded from 128.54.18.48 on Thu, 26 May 2016 21:08:16 UTC
All use subject to http://about.jstor.org/terms
Wilbur and Zhu: Click Fraud
Marketing Science 28(2), pp. 293-308, ©2009 INFORMS 295
the consumer's search results or Web page content. first page of ads, and 23% do not read past the first
If the consumer clicks on the advertiser's ad, she is few ads. He also noted that consumers often refine
redirected to a Web address chosen by the advertiser, their search if they do not find a good ad among
and the advertiser is charged a fee. Advertising costs the first few slots. Chen and He (2006) find that a
and quantity of searches available vary widely across higher ad listing sends a quality signal to uninformed
keywords. consumers. Rutz and Bucklin (2007a) and Ghose and
The cost-per-click business model was pioneered Yang (2007) demonstrate empirically that higher ad
by GoTo.com, which was later renamed Overture positions result in higher conversion rates,
and acquired by Yahoo!. Overture sold keywords Other forms of online advertising include cost per
in a public-information, first-price auction. It later thousand (CPM), in which websites are compensated
changed its auction mechanism to a private-value on an impression basis, and cost per action (CPA),
variation on Vickrey's (1961) second-price auction, in which advertisers pay per sale or lead. Prasad
the generalized second-price auction described by (2007) discussed "impression fraud," a problem in
Edelman et al. (2007). Google adopted the CPC auc- CPM advertising that is conceptually similar to click
tion in 2002, and introduced the use of consumers' fraud but operationally different. CPA advertising has
"click-through rate" (CTR), the number of consumers the potential to resolve click fraud concerns, but has
who clicked on the ad divided by all consumers who a principal/agent problem in which advertisers are
saw the ad, as an element in its auction mechanism incented to conceal customer leads and conversions
(Battelle 2005). Google's early ad-ranking algorithm from the search engine. Google piloted a CPA beta test
was the product of advertisers' per-click bid and in 2007, but participating advertisers were required
click-through rate (Goodman 2006). In 2005, Google to use Google software to track their conversions,
changed its auction mechanism to include a "quality It may be that if advertisers reveal enough revenue
score" that included CTR and additional predictors of information to the search engine to resolve the princi
consumer response to ads (such as the match between pal/agent problem, the search engine would be able
ad text and search term). Yahoo! introduced elements to design its auction mechanism to extract maximal
of consumer acceptance into its auction in 2007. Nei- advertising revenues. We speculate that CPA will can
ther Google's or Yahoo!'s current auction mechanism nibalize some CPC revenues, but we do not expect it
is publicly known (Gupta 2007). to completely replace the CPC business model.
The market leaders are Google, Yahoo!, and
Microsoft, with 66%, 21%, and 5% of clicks, respec- 2.2. Types of Click Fraud
tively.2 Google receives about 75% of paid search Search advertisers are charged when their ads are
advertising revenues.3 clicked, regardless of who does the clicking. Clicks
Keyword prices vary according to advertiser prof- may come from potential customers, employees of
itability, media competition, and keyword charac- rival firms, or computer programs. We refer to all
teristics. Although not representative, the keyword clicks that do not come from potential customers as
"mesothelioma attorney" cost an average of $35 per click fraud.
click, but region-specific keyword costs reached as Click fraud is sometimes called "invalid clicks" or
high as $80 per click (Goldfarb and Tucker 2007). "unwanted clicks." This is partly because the word
Rutz and Bucklin (2007b) illustrate the dramatic dif- "fraud" has legal implications that may be difficult
ferences between keywords containing branded and to prove or contrary to the interests of some of
generic terms. In a search advertising campaign for the parties involved. Google calls click fraud invalid
a hotel chain, branded keywords on Google created clicks and says it is "any clicks or impressions that
3.5 million impressions, with a click-through rate of may artificially inflate an advertiser's costs or a pub
13.3% and a cost per reservation of $2.76. Generic lisher's earnings... [including] a publisher clicking on
keywords generated 19.9 million impressions, with a his own ads, a publisher encouraging clicks on his
click-through rate of 0.3% and a cost per reservation ads, automated clicking tools or traffic sources, robots,
of $61.71. or other deceptive software."4
There is some evidence that higher ad positions There are two main types of click fraud:
are more desirable because not all consumers read • Inflationary click fraud: Search advertisements
through all of the ads. For example, Wilk (2007) often appear on third-party websites and compensate
reported that 62% of all searchers do not read past the those website owners on a per-click basis or with a
share of advertising revenues. These third parties may
22 SSoouurrcce,e ,h htttpt:p//:/h/ithwitiswe.icsoem.c/odmat/adceanttaecre/nsteearr/chseenargcinheeanngaliynseisa.npahlpy.sis.php. click the ads to inflate their revenues.
AAcccceesssseedd FFeebbrruuaarryy 22000088..
33 SSoouurrccee,, hhttttpp:/:///wwwwww.m.micircorsoosfotf.tc.ocmom/p/rpersespssapssa/ssp/rpesrse/s2s/00280/0f8e/bf0e8b/08/ 4 S4o Suorucrec, eh, thttptsp:/s:/ /w/wwww.wgo.googolge.lceo.cmom/a/dasdesnenses/e/susuppppoorrtt//bbiinn//aannsswweerr..ppyy
0022--003s3tsatteamteemnte.mnstp.mx. sApcxce.s sAedc cFeesbsreudar yF e2b0r08u.ary 2008. ?answer = 1?a6n7s3w7e.r A= c1c6e7s3s7e. dA cFceesbserdu Faerbyr u2ar0y0 82.008.
This content downloaded from 128.54.18.48 on Thu, 26 May 2016 21:08:16 UTC
All use subject to http://about.jstor.org/terms
Wilbur and Zhu: Click Fraud
296 Marketing Science 28(2), pp. 293-308, ©2009 INFORMS
• Competitive click fraud: Advertisers may click advertisers are not charged for this activity."5 We sur
rivals' ads with the purpose of driving up their costs mise it is especially difficult to detect invalid clicks if
or exhausting their ad budgets. When an advertiser's they come from IP addresses that are used by many
budget is exhausted, it exits the ad auction. A com- people or if the invalid clicks are designed to resem
mon explanation for competitive click fraud is that ble clicks generated by normal human use.
firms have the goal of driving up rivals' advertís- Most search engines claim to offer advertisers some
ing costs, but such an explanation may not be sub- protections against click fraud, although they do
game perfect. If committing competitive click fraud is not explain specifically how they identify fraudulent
costly, then driving up competitors' costs comes at the clicks. Tuzhilin (2006) defined the "fundamental prob
expense of driving down one's own profits. A more 'cm of click fraud prevention": A search engine can
convincing explanation may be found in the structure n°t explain specifically how it detects click fraud to
of the ad auction. When a higher-bidding advertiser its advertisers without providing explicit instructions
exits the ad auction, its rival may claim a better ad to unscrupulous advertisers on how to avoid detec
position without paying a higher price per click. tion. Advertisers are forced to either blindly trust that
There are myriad other types of click fraud, such as search engines seek to prevent click fraud or they may
fraud designed to boost click-through rates, to invite hire third-party firms to detect click fraud and pursue
retaliation by search engines against rival websites, refunds for any such fraud detected,
or to do malicious harm based on philosophical or Empirical research on click fraud s effects will have
economic grounds. These other types are thought to two challenges. The first challenge is that proba
be relatively infrequent, so we do not consider them bilistic judgments are required to detect click fraud,
• .1 • because a smart click fraudster would design its
Kciptrl. ,--11 i i • T-i
fraudulent clicks to complicate detection. For exam
2.3. Advertiser Perceptions of Click Fraud pie, fraudulent clicks may be generated by a widely
Search advertisers say click fraud is troubling. Adver- distributed "botnet" (Daswani and Stoppelman 2007)
tising Age (2006) reported the following results of a and timed to mimic normal click activity. The second
survey of search advertising agencies: challenge is that if click fraud can be detected by the
"In your experience, how much of a problem is researcher, it also could have been detected by the
click fraud with regard to paid placement?" advertiser. Search engines' standard business practice
16% "a significant problem we have tracked" is to refund advertising expenditures when adver
23% "a moderate problem we have tracked" tisers Present evidence of undetected click fraud, so
35% "we have not tracked, but are worried" empirical evidence of click fraud's effects could be
25% "not a significant concern" impacted by advertiser detection of click fraud. We
2% "never heard of it" speculate that these concerns could be resolved by
analyzing data from a company that previously did
"Have you been a victim of click fraud?" not try to detect click fraud, or perhaps by using an
42% Yes experimental approach.
21% No
38% Don't know 3. a Baseline Model of Search
"What type of click fraud did you experience?" Advertising
78% Inflationary click fraud We begin with a simple setting to establish how the
53% Competitive click fraud market operates in the absence of click fraud. This
„ ...... . . . , . . . . aids interpretation of equilibrium results when we
• GO°glTPh"tly W g , 7 ? 7 Wh6n introduce inflationary and competitive click fraud in
it paid $90 million to settle a click fraud lawsuit, jater sect¿ons
Lane's Gifts v. Google (CV-2005-052-1 (Ark. Cir. Ct.,
Miller County 2006)), in July 2006. Google acknowl- 3.1. Clicks
edges and describes the risks posed by click fraud in We assume there is a fixed period of length one, n cus
its annual reports. tomers click, and clicks arrive at a constant rate 1/n.
Firm j e{ 1,2} receives 7r;W per customer click when
2.4. Click Fraud Detection and Prevention its ad is in the top spot, and tt]L otherwise. We define
Search engines do not claim that they can fully detect = n(Vjw _ as the total value to advertiser j of
click fraud. Google states: we use both automated remaining in the top spot for the entire period of time,
systems and human reviews, analyzing all ad clicks it must be that min(Ax, A2) > 0, else firms will never
and impressions for any invalid click activity that enter positive bids.
may artificially drive up an advertiser's costs or a
publisher S earnings... . Our system enables US to fil- 5 Source, 5h Stotuprsc:e/,/ hwttwpws:/.g/owowgwle..gcooomgl/e.acdomse/nasdes/ensusep/psourptp/orbti/nb/iann/sanwsewre.rp.ypy
ter out most invalid clicks and impressions, and our ?answe r?=an97sw18er&=c9t7x18=&sicbtxli=nsigb.l iAngc.c eAscsceedss eFde bFerburaurayry 2 2000088..
This content downloaded from 128.54.18.48 on Thu, 26 May 2016 21:08:16 UTC
All use subject to http://about.jstor.org/terms
Wilbur and Zhu: Click Fraud
Marketing Science 28(2), pp. 293-308, ©2009 INFORMS 297
3.2. Search Advertising Technology 3.4. Equilibrium
Each firm enters a bid per click, bj, for a single adver- We analyze second-stage profits, then first-stage
tising slot sold by a monopoly gatekeeper. The high actions. When firm j wins the auction (W), its profit is
bidder claims the slot and pays the low bidder's bid
per click.6 We assume the two firms' ads have iden- njW(bk)
tical click-through rates, so the high bidder wins the
n(irjW — bk) when K; > n
top ad position. The high bidder then enters a capac
K: ( K:\ (i)
ity/ Kj> 1, the maximum number of clicks for which it
is willing to pay. If the total number of clicks exceeds riTTjyj —--}-1 1 JnVjL — bkKj when Kj<n,
Kj, the high bidder exits the advertising market when
its capacity has been exceeded. The low bidder then where K¡/n is the fraction of customer clicks firm j
claims the top spot at the next-highest advertiser's receives while on top, in the event it does not remain
per-click bid, which we normalize to zero. We assume on top for the entire time period. If firm k wins the
that each bidder knows its rival's value per click. auction and sets a capacity Kk > n, firm j receives
Given that the advertiser's maximum expenditure II;L = W77)L.
is the product of K and b, the advertiser's capac- In the first stage, each firm will anticipate the
ity choice is equivalent to choosing an advertising second-stage outcome and choose the bid b that
budget, as is required by all major search engines makes it indifferent between winning and losing the
(Google, Yahoo!, MSN). In the absence of an ad bud- auction. Thus, bj is chosen to equate UjW(bj) = IT,, ,
get, we presume that an advertiser could choose We summarize equilibrium behavior in Proposi
to stop remitting payments to the search engine at tion 1.
some point, which would give the same effect The Proposition L ln the absence of cUck fmud/ firm j
capacity-setting assumption simplifies the analysis, Uds A , ^ md wins the advertising auction if
but the results are unchanged under a budget-settmg ^ > ^ m flucho„ wmmr mmms on top for the mtne
assumption. p'me period and earns a profit of nrrm - Ak. The gatekeeper
Edelman et al. (2007) showed that with two bid- earns min{A A }
ders and one slot, the generalized second-price auc
tion reduces to a Vickrey second-price auction. We Proofs of all lemmas and propositions are in the
will appeal several times to the standard result that in appendix. Proposition 1 serves as a useful benchmark
a second-price auction, a weakly dominant strategy is to which we compare equilibria under inflationary
for firms to bid their reservation price. ar|d competitive click fraud.
We have made two restrictive assumptions here:
each firm knows its rival's profits from advertising, 4 Search Advertising with
and the firms have identical click-through rates. We ' Inflatio Clkk Frau(j
relax both of these assumptions in §6, when we con- TA7 . , , J. n ,. . , , . , ,.
., ,. , ,r ,i , , , , ,, , We now introduce inflationary click fraud into the
sider an auction mechanism that takes click-through J
baseline model. Major search engines pay third-party
rates into account.
websites to display search ads relevant to their site
content. Inflationary click fraud results when those
3.3. Structure of the Game
website owners click the ads to inflate their advertis
The game is played in two stages. First, each firm
, , , , , • • • • , mg revenues,
enters a bid per click and observes its position, with We first anal the indivldual website's problem of
the high bidder in the top spot. The high bidder choosi a dkk fraud leveL Next, we solve for equi
observes the low bidder's bid, the amount it must pay librium bids and capacltieS/ given a known amount of
per click. In the second stage, the high bidder chooses inflationary click fraud_ Finally/ we consider the case
its capacity. The reason for this structure is that, m of stochastic inflationary click fraud,
reality, the high bidder may observe its payment per
click (the low bidder's bid) immediately, but the low 4.1. Websites' Choice of Inflationary Click Fraud
bidder may only discover its rival's capacity if it has Ads associated with a particular keyword are placed
been exhausted. We seek a subgame-perfect equilib- Dn I third-party websites, indexed by w. We con
rium in pure strategies under full information: each sider two different compensation schemes. If web
firm anticipates its rival's action. site w is paid yw per click generated, its revenues
are yw(nw + rw), where nw is the number of customer
so c v 1 ,, -r,. . , , clicks generated through the website, and r is its
66 R eRsueltss uinl §t§3s- 5 icnon t§in§u3e t-o5 h ocldo inf tthien auucteio nt woi nhnero lisd d etiefr the auction winner is deter- . 0 ° .
mmiinneedd b byy t hteh ead avdervteirsitnigsi nbugd bgeutd rgaetth erra tthheanr btyh aan c obmyp aa rcisoomn poafrison of inflationary click fraud level. If website IV IS paid a
ppere-crlic-kc blidisc aklon eb. ids alone. fraction 8W e (0,1) of the ad revenues it generates,
This content downloaded from 128.54.18.48 on Thu, 26 May 2016 21:08:16 UTC
All use subject to http://about.jstor.org/terms
Wilbur and Zhu: Click Fraud
298 Marketing Science 28(2), pp. 293-308, © 2009 INFORMS
its revenues are 8wb(nw + rw), where b is the adver- large, software could be designed to accomplish this
tiser's payment per click, b does not vary across web- task.
sites and is a function of inflationary click fraud, with Although a revenue-sharing compensation scheme
db/drw <0. (We show in §4.2 that db/d{fPw rw) < 0 in suggests an equilibrium relationship between bids
equilibrium under certain conditions.) and inflationary click fraud levels, we are not
We assume that the cost of rw fraudulent clicks is going to model this relationship explicitly. Current
an increasing and convex function cw(rw), because a search engine policies make information transmission
greater number of fraudulent clicks increases the risk between websites and advertisers prohibitively dif
that the search engine will detect the fraudulent activ- ficult. Search engines do not reveal the distribution
ity. The search engine could then retaliate by exclud- of yw or 8W to either side. In addition, websites do
ing the website from its content network or initiating not know b, and advertisers do not know cw(rw),
a costly legal action against the website if click fraud nor how they vary across websites or advertisers,
constitutes a breach of contract. (However, note that websites need not know db/drw
Under a per-click compensation scheme, website exactly for Proposition 2 to hold; they need only
w's profits are know db/drw < 0.) Finally, advertisers have only lim
ited information about where their ads will appear,
ttw = max yw{nw + rw) — cw(rw), (2) and website owners do not know in advance what
ads will appear on their sites,
yielding a first-order condition yw = c'w(r*w) and a We proceed under each of two assumptions: Either
choice of r^ = c'~1(yw) in equilibrium. both advertisers can anticipate the inflationary click
Under a revenue-sharing compensation scheme, fraud level r = Y,w rw or they share a common belief
website w's profits are /(r) about its distribution. Advertisers may share a
common belief about /(r) because they both observe
ttw = max 8wb(nw + rw) — cw(rw) (3) the low bidder's bid, which is the only bid that is
paid, so it is the only bid that could influence r.
and site w's first-order condition, 8wb + 8w(nw + rw) ■ Next, we analyze the equilibrium effects of infla
(idb/drw) = c'w(rw), yields a unique r*w. tionary click fraud on advertisers' bids.
Proposition 2. Holding click fraud constant, for yw= 4.2. Deterministic Inflationary Click Fraud
8wb, per-click and revenue-sharing compensation schemes We assume that customers generate n = n0 + nw
yield identical payouts to websites. Allowing for endoge- ciicks, where n0 is the number of customer clicks that
nous click fraud, the revenue-sharing compensation scheme come directly from the search engine. Website own
will reduce inflationary click fraud, because it incents con- ers generate r fraudulent clicks. Both advertisers can
tent network partners to partially internalize the effect of anticipate r. We relax this assumption in §4.3.
inflationary click fraud on advertisers' bids. „ ^
4.2.1. Equilibrium. Equation (4) gives firm / s
The larger the derivative db/drw is in absolute value, profit when it wins the auction,
the less inflationary click fraud the third-party web
sites will produce. Search ads are typically displayed nVjW — bk(n + r) when Kj>n + r
on a large number of websites in search engines' con K: ( Kj \
tent networks, suggesting that \db/drw\ is small. The n¡w(bk) =
nniw ffflTr + (i - ^¿7 J nvlL - bkKi (4)
implications of this result for search engines are clear:
click fraud is reduced when search ads are not rotated when K¡ <n+r.
across a large number of websites, and each website .
is compensated with a percentage of the advertising first segment of the profit function represents
revenues it generates. the outcome in which firm 1 staYs °n toP for the
If Pb/drl > 0 (we later show d2b/d(Za rw)2 > 0 entire time Pedod- second se§ment occurs if firm
under certain assumptions), then db/drw is greatest ' s caPacity Wl11 be exhausted at some point, in which
in absolute value when I = 1. Thus, websites' incen- casf * 15 on }°f for nWn + r» customer clicks,
tives to internalize the effects of their inflationary click and has exited the auc,tlon for the remammS ^ " V
fraud on search engine revenues are maximized when r^n custcaner c 1C s'
other sites' click fraud levels do not affect their share Proposition 3 summarizes equilibrium behavior.
of advertising revenues. This suggests that search Proposition 3. When inflationary click fraud is deter
engines should allow advertisers to enter site-specific ministic and known to both bidders, and there is no corn
keyword bids bw to maximally reduce sites' incentives petitive click fraud, firm j bids Afl(n + r) and wins the
to engage in click fraud. Although it may be difficult advertising auction if A • > A^. Advertisers reduce their
for a human to manage, site-specific bids when I is bids by a proportion of r/(n + r), pricing out the effect of
This content downloaded from 128.54.18.48 on Thu, 26 May 2016 21:08:16 UTC
All use subject to http://about.jstor.org/terms
Wilbur and Zhu: Click Fraud
Marketing Science 28(2), pp. 293-308, ©2009 INFORMS . 299
click fraud. Firm j remains on top for the entire time period Fig uFrigeu r1e F1i rFmirm j' s/ 'Ps rPorfofitit FFuunnccttiioonn
and earns a profit of niTjW - Ak. The gatekeeper's revenues
njy,
are minjAj, A2}, as in the baseline model.
The auction mechanism completely internalizes the
effect of inflationary click fraud when the number of
fraudulent clicks is known to both bidders. Adver
tiser profits are unaffected; bids adjust endogenously
to counter the detrimental effects of the fraudu '%
lent clicks. The gatekeeper's revenues are unchanged,
although its profits must fall if it makes larger trans
fers to third-party websites. " ~KJ
Note. It also might be that n1lv is increasing everywhere above n.
4.3. Stochastic Inflationary Click Fraud
It is perhaps more intuitive to assume that advertís- por ^ > n
ers do not know how many fraudulent clicks will
occur because they may not know where their ads dIT/VV
will appear, or the distribution of 8W, yw, or cw(rw) ~3K~ ~ MR(K¡) — MC(Kj)
across websites. We assume here that advertisers max- 1
imize expected profits under a common belief about _ f °° A/ r,^ n _ p^jp _ n\i (6)
the probability density f(r) of the inflationary click JK¡-n n + r k '
fraud level r.
Both MR(Kj) and MC(K ) are decreasing in K .
4.3.1. Capacity Choice. We now add uncertainty Firm ; wiU chooge a K larger than „ if /~(A./(n +
about r into firm j s profit function. If Kj < n, firm r))f(r) dr > bk. This holds in equilibrium when b¡ > bk.
j s capacity will be exhausted for any realization of r. j/. js therefore determined by the first-order condition
When K¡ > n, firm j's capacity is only exhausted for on the second segment of the profit function.
some realizations of r. Equation (5) displays firm j's
profit function when it wins the auction. r°° A,
/ —hf(r)dr-bk[l-F(Kj-n)]>0. (7)
JK:-n n + r
n,w(M
jp Kj will be finite if MR(Kfi crosses MC(Kfi.
/ niTjW—^—bkKj At Kj = n, MR(K¡) is above MC(Kj) and steeper
^0
than MC(Kj). As K, increases, dMR(Kj)/dKj =
i
when K. < n -(A/Ky)/(X;. - n) and dMC(Kj)/dKj = bkf (K¡ - n), so
f(r)dr
MTjL
n + r I MR(Kj) later becomes flatter than MC(Kf). If MR(Kj)
K._n does not cross MC(K;), K( = oo.
Jo ^k(n+r)]f{r)dr (5) lemma 1. When {7) holds with equality, Kj is unique.
+ f°° \mr■ ' b K Figure 2 shows the case when K¡ is finite. If Kj < oo,
V„L ;W" + r ; X( is increasing in A;.
+ (!-lL)nir ]f{r)dr when K,>n. 43-2" Bids- As before' calculjatfr bi asuthe Per"
V n + r) ' J ' click payment that makes firm ] indifferent between
acquiring the advertising right and not acquiring it.
The uncertainty in the first segment of the profit func
tion concerns the number of customer clicks for which
the firm will remain on top. On the second segment of F'9u Frieg u2r eF 2ir Fmir mi' sy C's hCohiociece ooff KK,j
the profit function, the first term is the firm's expected
profits when it remains on top, weighted by the prob
ability that r is small enough that firm j is never f ^fidF(r) i mr(K)= j % f fir) dr
MR(K;)= J -d-rf(r)dr
knocked off. The second term is the firm's expected \ Ki~ Knr
profits in the event that its capacity is exhausted,
weighted by the probability that r is large enough to MC(Kj) = bk[l-F(Kj-n)]
exhaust the firm's capacity.
Figure 1 depicts II;W. For K¡ < n, n;VV changes linear
ly with Kj at a constant rate /0°°(A;/(n + r))f{r) dr — bk.
This content downloaded from 128.54.18.48 on Thu, 26 May 2016 21:08:16 UTC
All use subject to http://about.jstor.org/terms
Wilbur and Zhu: Click Fraud
300 Marketing Science 28(2), pp. 293-308, ©2009 INFORMS
Thus, bj is found by setting ILw(fr;) = II;L. We consider What we learn in this section is that inflationary
two cases: n < K¡ < oo and = oo. click fraud does not harm advertisers in a second
In the first case, K, will be finite when the firms price auction when they know exactly how much to
are sufficiently similar that MC (K) does not lie every- expect; this seemingly verifies the executive's com
where below MR(K). To aid interpretation of the ment that perhaps no solution to click fraud is nec
results, we assume symmetry between the two firms, essary. However, under the more realistic assumption
A■ = Ak — A, implying K¡ — Kk — K and b¡ = bk — b. We that firms face uncertainty in the level of inflationary
find b by equating firm j's expected winning profits click fraud, we see two things. First, search engines
to its expected losing profits, but we now must con- certainly have a strong incentive to detect and limit
sider that when firm j loses, it will claim the top spot click fraud in very competitive keyword auctions. See
when n + r > Kk. Thus, ond, when keyword auctions are less competitive, it
may be in the gatekeeper's interest to allow some
/,» iK\ —— nri click fraud.
n
ljW ■ J [mrjw-b(n + r)]f(r)dr
+ r (a_L- + nniL - bK)f(r)dr, (8) 5- Search Advertising with
JK-n\ n + r J Tnflatinnarv and Cnmneti
Inflationary and Competitive
Click Fraud
UjL = f (mrjL)f{r)dr
We have previously considered the effects of third
r°° / K \ party invalid clicks on market equilibria. Now we
JK-n \nTriw ~ ^ n -f r j — ^ extend the analysis to consider what happens when
the low bidder may click the high bidder's ad to
and b is determined by the equality of I1;VV and fl;X. hasten the high bidder's exit from the advertising
Proposition 4. When inflationary click fraud is auch°n
. , ,. .... ,. , c j , We start by proving our earlier assertion that com
stochastic, there is no competitive click fraud, and firms are .,. , ,
, , , ,. ., v , j .1 petitive click fraud may not be subgame perfect. In a
identical and set a finite K, expected gatekeeper revenues ,,, , , , ■ „ ■ r
. . „ . ,, ,. , f. j , r model where the number of inflationary fraudulent
are strictly lower than the baseline model. ,. , . . , , , , J . .
J clicks is known and the number of competitive fraud
In the second case, firm j wins and sets a capacity ulent clicks is rationally anticipated, the high bid
Kj = oo. This occurs when A; — Ak is sufficiently large der will shade its capacity upward in equilibrium.
that MR(Kj) lies everywhere above MC(K;). Assuming that click fraud is costly, the low bidder
„ _ „o . „ . ,. , . , . then will not commit any competitive click fraud.
Proposition 5. When inflationary click fraud is , Cr» , ., . . . , • ,, , , ,
/. +. , J, , fn §5.2, we show that uncertainty in the total num
ir'M/inii/' 4-Vtn-v/~> -if fi r\ /intti-M/ií'iíi'ri/» /im/i fliii 1 sin ^
stochastic, there is no competitive click fraud, and the los
ber of clicks may lead to competitive click fraud in
ing bid is sufficiently low that the high bidder sets = oo,
equilibrium. Competitive click fraud unambiguously
expected gatekeeper revenues are strictly higher than the
decreases advertisers' bids, but it also may increase
case when inflationary click fraud is deterministic.
the high bidder's budget.
Uncertainty about the amount of inflationary click Assumptions About Competitive Click Fraud. We
fraud may either increase or decrease gatekeeper rev- assume that the low bidder chooses a level of com
enues. It is likely to lower gatekeeper revenues when petitive click fraud, z, at cost c(z). We assume that
firms incremental profits of winning the auction are c(z) is increasing and convex because a larger num
similar. In such situations, for example in auctions for ber of clicks will increase the probability that the high
generic keywords, bidding is more intense and the bidder or the gatekeeper can verify the identity of
auction winner realizes a smaller profit from winning the firm committing click fraud and retaliate (e.g.,
the auction. Low profits induce the auction winner to through civil lawsuits or business channels).7
strategically limit its capacity to avoid paying for a We assume the low bidder chooses z simultane
large number of fraudulent clicks. ously with the high bidder's choice of K. The total
Gatekeeper revenues may rise with inflationary
click fraud when one firm's profits of winning are 7. ,. , ,. , , ,
, . r . °. One might also posit a com 7 pOnee tmiitghitv aels o cpolsiict ka c omfpretaituivde clcicok sfrta udf cuosnt fcutnictoionn
much larger than its rival s (for example, in auctions c(z, r), w hc(ezr, er )d, cw/hderr e< doc, /tdor a<l l0o,w t of oalrlo twh ef oprr tohbea bpirloitbyab oilfit yco omf pceotmipeti
tor branded keywords). In this case, the high bidder tive click ftirvaeu cdl icdke tfercatuido nd ettoec ftiaolnl wtoi tfhal li nwfitlhat iinofnlaartiyo ncalriyck c lficrka ufdra. uWd. eWe
gains very large rents in the baseline model, and its expect etxhpaetc tt hthea tt wthoe ttywpoe tsy opfes colfic ckl icfkr afurdau dca cna nb eb ei ninddeeppeennddeennttlyly
detected, given that website owners' fraudulent clicks will come
rents are SO large that it never chooses to strategi- detected, given that website owners' fraudulent clicks will come
11 i- .... •« /""»i* i t j .i i ,i exclusively from th eeixrcl uosiwvenly fsriotmes t,h ewirh oewrne saitse sc, owmherpeeast ciotmivpeet ictilviec ckli cfk rfarauudd
cally limit its capacity. Click fraud may then have the , u • , • T,
J c - r i • c 1S more hkely to occur on iss emaorrec lhike ley ntog oiccnure son msearacihn en gpinaegs' emsa.in Tpahgees. Trhee sruesullttss
effect of transferring some of the winner S profits to presente dp rbeseelnowte da rbee lqowua lairtea tqiuvaeliltya tuivneclyh aunngcehda nugnedd eurn dthere tahses uamssupmtipotnion
the gatekeeper. that c(z) = ctha(tz c(z,) = rc(z,) r.).
This content downloaded from 128.54.18.48 on Thu, 26 May 2016 21:08:16 UTC
All use subject to http://about.jstor.org/terms
Wilbur and Zhu: Click Fraud
Marketing Science 28(2), pp. 293-308, ©2009 INFORMS 301
number of clicks is now z + n + r. We seek a rational Ü;W is continuous at K¡ — n + zk, although its slope
expectations equilibrium in pure strategies under full falls at this point.
information: each firm anticipates its rival's action. The problem facing firm k in the case that it loses
is choosing zk to maximize
5.1. Deterministic Inflationary and
Competitive Click Fraud f °° r
/ \n7TkL C(Zk)
In the case that r is deterministic and known to both Jo L n + zk + r
firms, firm j's profit when it wins the initial auction is
+ (1 f(r) dr
V n + zk + r J
n;-w(M
nirjW-bk(n+zk+r) when Kj>n+zk + r ^ _ when Kj <n + zk
, Kj-n-Zk
K: ( K.
n7r^7zrz-+(1-7ZTi: <10) / [n^ki ~ c(zk)]f(r) dr
n+zk + r h (V 1 n+zk + r J o
AkK¡
when Kj <n+zk+r. + f n^k]N CiZk) f(r)dr
JJkK.j-n-zk w n + zk + r
Firm k's profit when it loses the initial auction is
when Kj>n + zk
(13)
mrkL - c(z.) whenK>« + zt + r ^
' UkL is continuous at K} = n+zk although its slope falls
Kj ( Kj \ at this point.
n ki — niTki. , — . + (1-- , r . ..)niTkw-c(zk)
11 + zk +r V n + zk + rj Proposition 7. Under stochastic inflationary click
when Kj < n + zk + r. fraud, gatekeeper revenues may be increasing or decreasing
(11) in the level of competitive click fraud z.
These profit functions are similar to those analyzed T.r „ _ , ., , ,
. _r„ . . ., .... . , , • We prove Proposition 7 for two special cases of the
in §4.2. Proposition 6 describes equilibrium behavior. , , . ,.
r 1 model in the appendix.
Proposition 6. When both firms know the inflation- The presence of both uncertain inflationary and
ary click fraud level r, if firm j wins the auction, then competitive click fraud limits the high bidder's ability
in equilibrium K¡>n + zk + r and zk — 0. Firm j never to react to either one. The high bidder mitigates infla
loses the top spot, and firm k therefore does not engage in tionary click fraud by limiting its capacity to protect
competitive click fraud. against paying for a large realization of r. The high
bidder mitigates competitive click fraud by increasing
5.2. Stochastic Inflationary and Competitive its capacity, to prevent the low bidder from knock
Click Fraud jng q Gff with a large z. Thus, when we add both
Here, we set up the problem under the general distri- types Qf fraud into the model, the auction win
bution f{r) and discuss results and intuition from the ner cannot respond optimally to either one without
full model. We describe the set of equilibria in pure being hurt by the other. What we learn in this section
strategies in the Technical Appendix, which can be js that search engine revenues may rise with compet
found at http://mktsci.pubs.informs.org. itive click fraud.
5.2.1. Profits. As before, there are two parts to
firm j's profit function. When K¡ < n + zk, firm j is 6< Asymmetric Click-Through Rates
always knocked off the top spot. When Kj > n + zk, Search engines commonly use advertisers' CTRs in
firm j is only knocked off for some realizations of r. conjunction with per-click bids to determine ad posi
tion listings (Rutz and Bucklin 2007a). It is there
iw' k' fore interesting to consider whether our main results
r°° / Kj \ would change under a more realistic keyword auc
J0 w)~ñ~+z +7 + n7r>L ~ k ') T fi°n. We consider here the auction mechanism used
by Google from 2002 to 2005, the last publicly known
when Kj < n -r ¿k auction mechanism used by that company.
»-H A related analysis is Katona and Sarvary (2007),
Í
[nVjW — bk{n + zk + r)]f(r) dr (1 ) whjcq provides necessary conditions for equilibrium
Jo
strategies in a multiunit click-through auction. How
p A ,K,
+ ' ' + niTji - bkKj f{r)dr ever, we are not aware of any previous papers to
Jk -n-zk _n + zk + r solve for dominant bidding strategies in an auction
when K,>n + zk. with a CTR component. We show that moving from
This content downloaded from 128.54.18.48 on Thu, 26 May 2016 21:08:16 UTC
All use subject to http://about.jstor.org/terms